# Questions tagged [projections]

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### How combine multiple projections into a single pass?

We have a projector type display used in an automotive application, where a projector displays an application on the windshield. Because the projector would normally warp a flat image, we have to ...
31 views

### 3d Math Primer book equation derivation - Projecting One vector onto another

I'm reading the book 3d Math Primer for Graphics and Game Development 1st edition by Fletcher Dunn and Ian Parberry. On page 61 there's this: How does it derive $v_{||}$ there? It doesn't follow ...
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### What exactly is the orthographic projection used by Matlab

I would like to imitate the orthographic projection that Matlab uses by default: Matlab View Projections and Matlab camproj It seems similar to the "Trimetric" projection described here: ...
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### Projecting a point on a Freefrom surface

My first issue is getting a set of planes and a set of points as input, an find the projection of the those points on the nearest plane. That was pretty easy, where i just calculate the normal of the ...
46 views

### Can pixels on the image plane be mapped to world space coordinates?

I'm trying to learn the fundamentals of 3d computer graphics by writing a toy framework in WebGL. I'm currently working on mouse based camera controls. There are plenty of good resources in the ACM ...
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### What quad will fill the screen, which can be inverse-projection-view transformed to map to the near frustum plane?

I've been experimenting with raytracing using GLSL. I had success rendering a cube which encloses the object. Now I want to do a full-screen raytrace, and I want to construct a quad which covers the ...
54 views

### How to translate the center of an equirectangular projection?

I'm trying to perfectly align two or more equirectangular photos of the same place taken from slightly different positions. Using an example provided by openMVG I managed to get the relative position ...
359 views

### A question about derivation in oblique view frustum

Problem Description: Reference: Oblique View Frustum Depth Projection and Clipping "Mathematics for 3D Game Programming and Computer Graphics" 3rd edition, chapter 5.6. M is the original projection ...
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### Inverse texture mapping

I have a textured 3D object and looking for ways to transform back the texture. Effectively, I think this is an inverse texture mapping task. Do you know of anything close to this? Some papers or ...
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### What to reproject when doing temporal filtering in stochastic screen space reflection?

I am in the middle of implementing stochastic screen space reflection based on frostbite presentation here. On page number 39, it is stated that we need to reproject the ray intersection location ...
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### How to derive a perspective projection matrix from its components?

This has been haunting me for several days now. I want to find the component that makes up of this 4x4 perspective projection matrix, with $l$(left), $r$(right), $b$(bottom), $t$(top), $n$(near), $f$(...
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### WebGL Can't render anything, wrong projection?

I'm trying to understand and learn WebGL and computer graphics from button up, that is why I started to work on my own little library for that. I've spent couple of days looking for right answer and I ...
259 views

### 3ds max: Z-fighting when working with Large Objects

I had a z-fighting/z-clipping issue with a scene containing some very large objects yesterday in 3ds max. It can be seen in the image below: For some reason downscaling the scene significantly (a ...
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### Do straight lines always remain straight when projected with a perspective camera?

If I have a straight line in 3D space and I use a camera matrix to do a perspective projection into a 2D plane/screen will the resulting line always be straight too? If I project the start point and ...
1k views

### Why do GPUs divide clip space Z by W, for position?

Background: I found that it is very easy to use a linear depth buffer, using only a slight modification to the canonical vertex transformation. The simplest method is found at the bottom of https://...
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### Need help with change of basis (world to camera frame)

I'm reading up on coordinate systems and geometric transformations but the change of basis topic still confuses me. I found this exercise but, honestly, I wouldn't know how to begin: Given a world ...
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### Computing perspective directly

Assume the screen is axis aligned with origin at 0 and there is absolutely no view transformation. in other words we will simply try to project the model onto the screen plane following perspective. ...
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### Overlaying a grid on to a height map

What is the method used in overlaying a grid (agonostic of the grid type) on to a height map? It seems it's some sort of projection, but what are the technical details in how to implement it? An ...
187 views

### Project vertex onto plane

What I have: a plane given by its normal$\ n$ and a point on the plane$\ p$. a 3D-point$\ v$. a direction$\ d$. What I need: the projection of$\ v$ along$\ d$ onto the plane. How can I ...
373 views

### finding the projection matrix for one point perspective

I found the derivation for two point and three point perspective here on this site, even though it says review on one point perspective, it doesn't give a link to previous pages, but I'd like to ...
332 views

### perspective projection transformation matrix

In one text, the derivation for perspective projection goes like this: If $x',y',z'$ represent any point along the projection line,and $x_{prp},y_{prp},z_{prp}$ are the projection ...
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### How to compute A and B in projection matrix

I'm trying to compute a projection matrix to transform from view space to NDC with a near clip plane at -1 and far plane at +1. The general form of this matrix (disregarding aspect ratio and focal ...
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### How to generate the stereographic projection of a 3D model

Given a 3D model, is there a way to stereographically project it to a 2D image? In particular, I would only need a little more than half the model (the lower half) to be mapped to the plane (mapping ...
220 views

### What transformations should I apply to a model to produce this 3D effect?

I saw a video on YouTube where a person uses a transparant, knotted pyramid to display "holograms" using their smartphone. (I have not been able to reproduce this yet, so I can't tell for sure if it ...
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### Possible approach for product mockup creation including distortion created through perspective

I am not an expert in 3D nor computer graphics. Please forgive me if I use wrong wording. High level problem description: For an online shop, I would like to create mockup images of apparel (t-shirts,...
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### If a 3D scene is rendered onto a hemispherical display, will there still be warping near the edges?

When a 3D scene is rendered to a 2D display, the image is distorted near the edges of the display. If a 3D scene is rendered onto a hemispherical display, will there still be warping?
474 views

### How to unproject quadrilateral into rectangle?

tl;dr: Math problem in projective geometry: How does one find some 4x4 camera matrix that gives a projection as illustrated below, such that points A,B,C,D are somewhere on the edges of the unit box (...
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### Solving a problem from *Foundations of Computer Graphics*:

From Gortler's Foundations of Computer Graphics (i.e., self-study): Let $\mathbf{\vec{e}}^t = \mathbf{\vec{w}}^t E$ and let $P$ be a camera matrix that is just some arbitrary $4$ by $4$ matrix with ...
8k views

### Does a sphere projected into 2D space always result in an ellipse?

My intuition has always been that when any sphere is projected into 2D space that the result will always mathematically be an ellipse (or a circle in degenerate cases). In the past when I was ...
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### Determining slopes of lines in perspective projection

Suppose I have parallel lines running along the ground (into the horizon). If I have a camera and I know its tilt angle, is there a way to calculate the slopes of the lines as projected to the 2D ...
399 views

### Need a reputable source for the formula for the shape of Earth's horizon

What I'm asking for I stress that I am not asking for the formula---I know the formula, and how to derive it. Several different versions of it are reproduced near the end of the post. In fact, ...
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### The distance from the cube sides to the parallel projection plane

I have asked this question on ru.stackoverflow.com and have no valid answers. Specification: Coordinate system Cube spins around its center on all three axes. Turn angle is not known previously. ...
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### Projective texturing from many images

Problem: I'm trying to dynamically texture a mesh of the real world generated by the Hololens over time using photos also captured from the Hololens, perhaps one photo per second. Each of the photos ...
1k views

### How to decompose projection matrix?

I want to decompose projection matrices into near, far, top, bottom, left and right values to create a bounding box for view frustum. I used the formula described in this site Decompose the OpenGL ...
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### 3D reconstruction using 2D matched points

I have 2 images, called left and right images. I have some matched points $[c_l,r_l]$ and $[c_r,r_r]$ in both of them (these points are in pixel coordinates). For a 3D point in the real world, they ...
90 views

### How would I convert a picture of a slanted surface into a straight one? [duplicate]

Suppose I took a picture of a whiteboard at an angle. If I could detect where the corners of the whiteboard are, what algorithms and linear projections could I use to convert this slanted view into a "...
34 views

### Program to visualize geodesics and linear projection of an ellipsoid simultaneously

I am trying to solve a problem in computer graphics but to do it I need to be able to see a comparison of geodesic lines and straigth line projections on the ellipsoid. I have not been able to ...
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### Make 3d objects from 3 projections in 3D Studio Max

In the early 3D Studio days before it got Max in its name it was possible to make a 3d object by defining its projections in xy, xz and yz plane. 3ds would then interpolate a 3d object from the ...
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### A way to save 360° panorama video

What is the best way to save video from faces of a cube? The render can produce 6 squares (90°x90°) of 1024x1024 resolution. Faces oriented along axies and only position is changed continuously. I ...
1k views

### Why are width and height divided by 2 in the perspective projection matrix?

I'm using OpenGL to learn computer graphics. I'm trying to understand projection matrices. The following are shown in the OpenGL 'Red Book': I don't understand why the width and height are divided ...
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### Compute area (not surface area) and perimeter of a mesh

I'm currently researching how to compute geometric properties of architectural shapes based on their 3D meshes, and am stuck for some time on the area and perimeter calculations. First, the area: ...
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### 3D projection that increases objects' size as they become more distant

tl;dr Is there a name for a type of (non-physical) projection that causes objects to become larger the farther they are from a camera? With a fisheye projection, an object twice as far from the ...
580 views

### Why is the back of a perspective frustrum larger than the front?

I'm following this tutorial on the perspective projection. Question: If the point of a perspective projection is to create the perspective effect (where objects faraway appear to be smaller): then ...
980 views

### How am I able to perform perspective projection without a near plane?

I'm learning about 3D computer graphics, but I'm having a hard time understanding why the near plane of a viewing frustum can not be placed at z position $0$ (right at the camera). I can understand ...
905 views

### Render with camera perspective off-center

So ordinarily we have this But I'm after this! Is it possible to do this? Ideally by changing the projection matrix? The reasoning is kinda interesting - I am developing for mobile VR, and I have ...
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### Getting from the default view volume to an image on the screen

I don't completely understand the last part of the MVP matrix (projection). In orthographic projection we simply scale the view volume into the default view volume (+-1 on all axis). In perspective ...
3k views

### understanding glm::perspective vs glm::ortho

I'm new to computer graphics. I played around with OpenGL and now am trying out Vulkan. Basically what I want to do, in 2D is have an 800x800 window, and I want that to represent 800 meters by 800 ...
153 views

### Calculate Camera parameters and HandEyeCalibration

I'm trying to calculate camera paramters and a hand eye calibration (Transformation from camera to eye (display) coordinates) for rendering on a see-through HMD. I have already calculated a ...